WannierSTM: Efficient superconducting scanning-probe spectroscopy from maximally localized Wannier functions

Abstract

We present a Python-based program that combines maximally localized Wannier functions-based first-principles electronic structure with the nonequilibrium Green's function formalism to enable efficient simulations of scanning tunneling microscopy (STM). The workflow builds upon standard density functional theory packages to construct compact transport Hamiltonians that preserve the properties of realistic materials. Superconductivity is incorporated via an effective pairing potential within the Nambu-spinor formalism, while coupling to the STM tip and substrate electrodes is treated using the wide-band limit approximation. Within this formulation, transport quantities such as current-voltage characteristics and differential conductance are evaluated in a closed analytical form. This avoids explicit numerical energy integrations and enables rapid spectroscopic calculations over broad parameter spaces. The framework provides a unified and computationally efficient approach for modeling superconducting hybrid nanostructures with spin-orbit coupling, magnetic textures, and spin polarization. Representative applications in spin chains, two-dimensional and molecular magnets on a superconductor demonstrate its robust capabilities for both simple model systems and realistic ab initio molecular structures relevant to modern STM experiments.